This invention relates to maintenance-free, non-pneumatic vehicle and cart tires, particularly intended for wheelchairs, pushchairs, tricycles, bicycles, trollies, carts, and gurneys.
Non-pneumatic tires offer important maintenance advantages over pneumatic tires. With non-pneumatic tires there is no need to check and adjust air pressure and there is never a worry about a flat or punctured tire, thus avoiding these common inconveniences encountered when using pneumatic tires. Especially for persons using wheelchairs, surveys show that tires are the biggest repair problem for all kinds of wheelchairs, see "Wheelchair III: Report of a Workshop" Bethesda, Md.: Rehabilitation Engineering Society of North America, 1982.
Solid and foamed rubber tires, which do not contain air under pressure, do not become dysfunctional when punctured. Here, the use of the word `rubber` is intended to cover that group of materials which has the ability to undergo large deformations and to recover quickly. However, solid rubber tires are extremely heavy, with a high rolling resistance, and have a very high spring constant, giving an uncomfortable ride. Foamed rubber tires offer improvements over solid rubber tires but are prone to cutting and destruction by fatigue failure due to the very low fatigue strength associated with foamed materials: Atkins, A. G., and Y-W Mai, `Elastic and Plastic Fracture`, E. Horwood Ltd., 1985, (p. 799).
All conventional tires, including standard pneumatic tires, are made in standard vulcanizing moulds, and a special mould is required for each size of tire. In addition, there are expensive complications in the moulding process such as mould cores and reinforcement materials being required.
U.S. Pat. No. 4,493,355 issued to Ippen et al., and assigned to Bayer Aktiengesellschaft, (hereafter: `the Bayer patent`) discloses a `puncture-proof` tire consisting essentially of a single vulcanisable material and comprising a tread thicker than the side walls, a continuous encircling empty space between the base and the tread, with the moment of inertia of the latter being at least six times greater than that of the side walls, and an encircling annular reinforcement of plastics material in the base, hardened after the tire is fitted on the rim of the wheel. This invention suffers from the disadvantages, inter alia, it is not possible to remove the tire from the rim, and this is inconvenient; that the maximum stresses in the tire material that may occur in practice are too high to give a satisfactorily long fatigue life; that its spring constant appears to be too low to cope with sudden very large deflections, i.e. on impact; and that it requires an extra (and, as will be demonstrated below, unnecessary) manufacturing step of introducing a hardenable plastics material.
Moreover, we have established that the Bayer patent is using oversimplified criteria for a very complicated problem. The moment of inertia ratio is calculated as follows. Assuming the load carried over a length of tire is b, the two moments of inertia I are given by: I.sub.tread =(1/12)b h.sub.t.sup.3 and I.sub.side wall =(1/12)b h.sub.sw.sup.3, where t stands for tread, sw stands for side wall, and h for height (thickness).
Thus, I.sub.t /I.sub.sw =h.sub.t.sup.3 /h.sub.sw.sup.3. For the Bayer patent design h.sub.t =11 mm, and h.sub.sw =6 mm; then, EQU I.sub.t /I.sub.sw =11.sup.3 /6.sup.3 =6.16.
The Bayer patent criterion (I.sub.t /I.sub.sw &gt;6) would suggest that the maximum stress under load would be similar for the tread region and the side wall region.
The Bayer patent's criterion, I(tread)/I(side wall)&gt;6, is related to the concept that the arching type cross-section acts like a bridge in bending, and to have the same bending stress everywhere in the arch requires that the thickness of the arch increase towards the top of the arch where the load is applied. Thus, I.sub.t must increase in comparison to I.sub.sw.
However, this ratio is not a required criteria for tire design. For example, one could let the side wall be 1 mm thick and still require I.sub.t /I.sub.sw &gt;6, but the tire would collapse under load.
We have discovered that it is not necessary to require I.sub.t /I.sub.sw &gt;6 for a satisfactory design. Using I.sub.t /I.sub.sw &gt;1 we were able to design the tire so that the maximum stress in the tire did not exceed the fatigue stress limit for long life.
For good tire design one must consider all of the physical phenomena involved: 1. contact stress theory, 2. thick walled cylinder theory, 3. rubber stress-strain properties, and 4. fatigue theory. In addition, one must consider a great number of other variables associated with compounding rubber. For example, the amount of wax to introduce into the compound is very important, etc. One method which we have used is the finite element analysis approach to tire design. This method takes into account most of the physical theory involved. Our results show that the Bayer criterion is not a real requirement for good design, and we find that I.sub.t /I.sub.sw &gt;1 will produce well designed tires.